Sevilla keeper Yassine Bounou saved spot kicks from Gianluca Mancini and Roger Ibanez, while Sevilla were flawless in their execution, scoring their first four.
The game had finished 1-1 after extra time.
Paulo Dybala gave the Italians the lead from a counter-attack in the 35th minute but Sevilla then took control of the game and found the equaliser thanks to an own-goal by Mancini in the 55th minute.
The win means Sevilla will compete in next season’s Champions League despite finishing outside the top four in La Liga.
AAP